Many-body interactions between contracting living cells

TL;DR

This paper models the complex mechanical interactions among living cells in tissues as active force dipoles within an elastic medium, revealing significant many-body effects that depend on cellular regulation behaviors.

Contribution

It introduces a nonlinear many-body interaction model for cells in elastic environments, highlighting the importance of higher-order effects in tissue mechanics.

Findings

Many-body interactions differ from pairwise sums depending on cell regulation.

Cells regulating their position exhibit smaller many-body energy than pairwise sum.

Non-regulating cells show larger many-body energy than pairwise sum.

Abstract

The organization of live cells into tissues and their subsequent biological function involves inter-cell mechanical interactions, which are mediated by their elastic environment. To model this interaction, we consider cells as spherical active force dipoles surrounded by an unbounded elastic matrix. Even though we assume that this elastic medium responds linearly, each cell's regulation of its mechanical activity leads to nonlinearities in the emergent interactions between cells. We study the many-body nature of these interactions by considering several geometries that include three or more cells. We show that for different regulatory behaviors of the cells' activity, the total elastic energy stored in the medium differs from the superposition of all two-body interactions between pairs of cells within the system. Specifically, we find that the many-body interaction energy between cells that regulate their position is smaller than the sum of interactions between all pairs of cells in the system, while for cells that do not regulate their position, the many-body interaction is larger than the superposition prediction. Thus, such higher-order interactions should be considered when studying the mechanics of multiple cells in proximity.